Recent advances in computational modeling of fibrin clot formation: A review

Venous Thromboembolism: Review of Clinical Challenges, Biology, Assessment, Treatment, and Modeling

Venous thromboembolism (VTE) is a massive clinical challenge, annually affecting millions of patients globally. VTE is a particularly consequential pathology, as incidence is correlated with extremely common risk factors, and a large cohort of patients experience recurrent VTE after initial intervention. Altered hemodynamics, hypercoagulability, and damaged vascular tissue cause deep-vein thrombosis and pulmonary embolism, the two permutations of VTE. Venous valves have been identified as likely locations for initial blood clot formation, but the exact pathway by which thrombosis occurs in this environment is not entirely clear. Several risk factors are known to increase the likelihood of VTE, particularly those that increase inflammation and coagulability, increase venous resistance, and damage the endothelial lining. While these risk factors are useful as predictive tools, VTE diagnosis prior to presentation of outward symptoms is difficult, chiefly due to challenges in successfully imaging deep-vein thrombi. Clinically, VTE can be managed by anticoagulants or mechanical intervention. Recently, direct oral anticoagulants and catheter-directed thrombolysis have emerged as leading tools in resolution of venous thrombosis. While a satisfactory VTE model has yet to be developed, recent strides have been made in advancing in silico models of venous hemodynamics, hemorheology, fluid-structure interaction, and clot growth. These models are often guided by imaging-informed boundary conditions or inspired by benchtop animal models. These gaps in knowledge are critical targets to address necessary improvements in prediction and diagnosis, clinical management, and VTE experimental and computational models.

Investigating clot-flow interactions by integrating intravital imaging with in silico modeling for analysis of flow, transport, and hemodynamic forces

As a blood clot forms, grows, deforms, and embolizes following a vascular injury, local clot-flow interactions lead to a highly dynamic flow environment. The local flow influences transport of biochemical species relevant for clotting, and determines the forces on the clot that in turn lead to clot deformation and embolization. Despite this central role, quantitative characterization of this dynamic clot-flow interaction and flow environment in the clot neighborhood remains a major challenge. Here, we propose an approach that integrates dynamic intravital imaging with computer geometric modeling and computational flow and transport modeling to develop a unified in silico framework to quantify the dynamic clot-flow interactions. We outline the development of the methodology referred to as Intravital Integrated In Silico Modeling or IVISim, and then demonstrate the method on a sample set of simulations comprising clot formation following laser injury in two mouse cremaster arteriole injury model data: one wild-type mouse case, and one diYF knockout mouse case. Simulation predictions are verified against experimental observations of transport of caged fluorescent Albumin (cAlb) in both models. Through these simulations, we illustrate how the IVISim methodology can provide insights into hemostatic processes, the role of flow and clot-flow interactions, and enable further investigations comparing and contrasting different biological model scenarios and parameter variations.

Identification of Genes and miRNAs Associated with TAFI-Related Thrombosis: An in Silico Study

Thrombin-Activatable Fibrinolysis Inhibitor (TAFI) is a carboxypeptidase B-like proenzyme encoded by the CPB2 gene. After thrombin activation, TAFI downregulates fibrinolysis, thus linking the latter with coagulation. TAFI has been shown to play a role in venous and arterial thrombotic diseases, yet, data regarding the molecular mechanisms underlying its function have been conflicting. In this study, we focused on the prediction and functional enrichment analysis (FEA) of the TAFI interaction network and the microRNAs (miRNAs) targeting the members of this network in an attempt to identify novel components and pathways of TAFI-related thrombosis. To this end, we used nine bioinformatics software tools. We found that the TAFI interactome consists of 28 unique genes mainly involved in hemostasis. Twenty-four miRNAs were predicted to target these genes. Co-annotation analysis of the predicted interactors with respect to Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways and transcription factors (TFs) pointed to the complement and coagulation cascades as well as neutrophil extracellular trap formation. Cancer, stroke, and intracranial aneurysm were among the top 20 significant diseases related to the identified miRNAs. We reason that the predicted biomolecules should be further studied in the context of TAFI-related thrombosis.

clotFoam: An Open-Source Framework to Simulate Blood Clot Formation Under Arterial Flow

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.

clotFoam: An open-source framework to simulate blood clot formation under arterial flow

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.

Chitosan-Based Biomaterials for Hemostatic Applications: A Review of Recent Advances

Hemorrhage is a detrimental event present in traumatic injury, surgery, and disorders of bleeding that can become life-threatening if not properly managed. Moreover, uncontrolled bleeding can complicate surgical interventions, altering the outcome of surgical procedures. Therefore, to reduce the risk of complications and decrease the risk of morbidity and mortality associated with hemorrhage, it is necessary to use an effective hemostatic agent that ensures the immediate control of bleeding. In recent years, there have been increasingly rapid advances in developing a novel generation of biomaterials with hemostatic properties. Nowadays, a wide array of topical hemostatic agents is available, including chitosan-based biomaterials that have shown outstanding properties such as antibacterial, antifungal, hemostatic, and analgesic activity in addition to their biocompatibility, biodegradability, and wound-healing effects. This review provides an analysis of chitosan-based hemostatic biomaterials and discusses the progress made in their performance, mechanism of action, efficacy, cost, and safety in recent years.

Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke

Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA₂DS₂-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction-known as Virchow's triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools-such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage-have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields.

Advances in Fibrin-Based Materials in Wound Repair: A Review

The first bioprocess that occurs in response to wounding is the deterrence of local hemorrhage. This is accomplished by platelet aggregation and initiation of the hemostasis cascade. The resulting blood clot immediately enables the cessation of bleeding and then functions as a provisional matrix for wound healing, which begins a few days after injury. Here, fibrinogen and fibrin fibers are the key players, because they literally serve as scaffolds for tissue regeneration and promote the migration of cells, as well as the ingrowth of tissues. Fibrin is also an important modulator of healing and a host defense system against microbes that effectively maintains incoming leukocytes and acts as reservoir for growth factors. This review presents recent advances in the understanding and applications of fibrin and fibrin-fiber-incorporated biomedical materials applied to wound healing and subsequent tissue repair. It also discusses how fibrin-based materials function through several wound healing stages including physical barrier formation, the entrapment of bacteria, drug and cell delivery, and eventual degradation. Pure fibrin is not mechanically strong and stable enough to act as a singular wound repair material. To alleviate this problem, this paper will demonstrate recent advances in the modification of fibrin with next-generation materials exhibiting enhanced stability and medical efficacy, along with a detailed look at the mechanical properties of fibrin and fibrin-laden materials. Specifically, fibrin-based nanocomposites and their role in wound repair, sustained drug release, cell delivery to wound sites, skin reconstruction, and biomedical applications of drug-loaded fibrin-based materials will be demonstrated and discussed.

Computational Analysis of the Related Factors of Deep Vein Thrombosis (DVT) Formation in Patients Undergoing Hip Fracture Surgery

A retrospective study was conducted on 51 patients undergoing hip fracture surgery to investigate the factors associated with the formation of deep venous thrombosis (DVT). The independent sample t-test and correlation analysis were used to sort out and analyze the data. The findings are as follows. (1) Different gender samples showed significant differences in the Caprini score and thrombus location. Most DVTs in females are located in the posterior tibial vein and intermuscular veins. The Caprini score of females was significantly higher than that of males. (2) Age displays a positive correlation with DVT, coronary heart disease, hypertension, and different surgical types, respectively. (3) There is a correlation between age and operation duration. (4) Hyperlipidemia and cerebrovascular disease show a positive correlation with DVT. (5) There was a significant negative correlation between the Caprini score and the quantification of D-dimer. This indicates that in this sample, the higher the patients' Caprini score is, the lower the quantitation of D-dimer will be. (6) Hyperlipidemia and cardiac insufficiency show a positive correlation with cerebrovascular disease. Patients with hyperlipidemia and cardiac insufficiency may also suffer from cerebrovascular diseases.

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

Models of Shear-Induced Platelet Activation and Numerical Implementation With Computational Fluid Dynamics Approaches

Shear-induced platelet activation is one of the critical outcomes when blood is exposed to elevated shear stress. Excessively activated platelets in the circulation can lead to thrombus formation and platelet consumption, resulting in serious adverse events such as thromboembolism and bleeding. While experimental observations reveal that it is related to the shear stress level and exposure time, the underlying mechanism of shear-induced platelet activation is not fully understood. Various models have been proposed to relate shear stress levels to platelet activation, yet most are modified from the empirically calibrated power-law model. Newly developed multiscale platelet models are tested as a promising approach to capture a single platelet's dynamic shape during activation, but it would be computationally expensive to employ it for a large-scale analysis. This paper summarizes the current numerical models used to study the shear-induced platelet activation and their computational applications in the risk assessment of a particular flow pattern and clot formation prediction.

An Accelerated Thrombosis Model for Computational Fluid Dynamics Simulations in Rotary Blood Pumps

Purpose

Thrombosis ranks among the major complications in blood-carrying medical devices and a better understanding to influence the design related contribution to thrombosis is desirable. Over the past years many computational models of thrombosis have been developed. However, numerically cheap models able to predict localized thrombus risk in complex geometries are still lacking. The aim of the study was to develop and test a computationally efficient model for thrombus risk prediction in rotary blood pumps.

Methods

We used a two-stage approach to calculate thrombus risk. The first stage involves the computation of velocity and pressure fields by computational fluid dynamic simulations. At the second stage, platelet activation by mechanical and chemical stimuli was determined through species transport with an Eulerian approach. The model was compared with existing clinical data on thrombus deposition within the HeartMate II. Furthermore, an operating point and model parameter sensitivity analysis was performed.

Results

Our model shows good correlation (R² > 0.93) with clinical data and identifies the bearing and outlet stator region of the HeartMate II as the location most prone to thrombus formation. The calculation of thrombus risk requires an additional 10–20 core hours of computation time.

Conclusion

The concentration of activated platelets can be used as a surrogate and computationally low-cost marker to determine potential risk regions of thrombus deposition in a blood pump. Relative comparisons of thrombus risk are possible even considering the intrinsic uncertainty in model parameters and operating conditions.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13239-021-00606-y.

Continuum modeling of thrombus formation and growth under different shear rates

Obstruction of blood flow due to thrombosis is a major cause of ischemic stroke, myocardial infarction, and in severe cases, mortality. In particular, in blood wetting medical devices, thrombosis is a common reason for failure. The prediction of thrombosis by understanding signaling pathways using computational models, lead to identify the risk of thrombus formation in blood-contacting devices and design improvements. In this study, a mathematical model of thrombus formation and growth is presented. A biochemical model of platelet activation and aggregation is developed to predict thrombus size and shape at the site of vascular injury. Computational fluid dynamics using the finite volume method is employed to compute the velocity and pressure fields which are influenced by the growing thrombi. The passive transport of platelets, agonists, the platelet activation kinetics, their adhesion to the growing thrombi and embolization of platelets are solved by a fully coupled set of convection-diffusion-reaction equations. The thrombogenic surface representing blood-contacting material or injured blood vessel was incorporated into the model as a surface flux boundary condition to initiate thrombus formation. The blood is considered as a Newtonian fluid, while the thrombus is treated as a porous medium. The results are compared with in vitro experiments of a microfluidic chamber at an initial inlet venous shear rate of 200s^-1 using a pressure-inlet boundary condition. The thrombus development due to agonist concentrations and change in the shear rate as well as thromboembolism for this benchmark problem is successfully computed. Furthermore, to extend the current model to a physiologically relevant configuration, thrombus formation in a blood tube is simulated. Two different heterogeneous reaction rates for platelet aggregation are used to simulate thrombus growth under a constant inlet flow rate. The findings show that the thrombus shape can be substantially altered by the hemodynamic conditions, increase in the shear rate and due to the combined effects of shear induced platelet activation and the heterogeneous reaction rates. It is also concluded that the model is able to predict thrombus formation in different physiological and pathological hemodynamics.

Microfluidic-based functional materials: new prospects for wound healing and beyond

Microfluidics has been applied to fabricate high-performance functional materials contributing to all physiological stages of wound healing. The advances of microfluidic-based functional materials for wound healing have been summarized.

Realistic computer modelling of stent retriever thrombectomy: a hybrid finite-element analysis-smoothed particle hydrodynamics model

Stent retriever thrombectomy is a pre-eminent treatment modality for large vessel ischaemic stroke. Simulation of thrombectomy could help understand stent and clot mechanics in failed cases and provide a digital testbed for the development of new, safer devices. Here, we present a novel, in silico thrombectomy method using a hybrid finite-element analysis (FEA) and smoothed particle hydrodynamics (SPH). Inspired by its biological structure and components, the blood clot was modelled with the hybrid FEA-SPH method. The Solitaire self-expanding stent was parametrically reconstructed from micro-CT imaging and was modelled as three-dimensional finite beam elements. Our simulation encompassed all steps of mechanical thrombectomy, including stent packaging, delivery and self-expansion into the clot, and clot extraction. To test the feasibility of our method, we simulated clot extraction in simple straight vessels. This was compared against in vitro thrombectomies using the same stent, vessel geometry, and clot size and composition. Comparisons with benchtop tests indicated that our model was able to accurately simulate clot deflection and penetration of stent wires into the clot, the relative movement of the clot and stent during extraction, and clot fragmentation/embolus formation. In this study, we demonstrated that coupling FEA and SPH techniques could realistically model stent retriever thrombectomy.

Numerical modelling of blood rheology and platelet activation through a stenosed left coronary artery bifurcation

Coronary bifurcations are prone to atherosclerotic plaque growth, experiencing regions of reduced wall shear stress (WSS) and increased platelet adhesion. This study compares effects across different rheological approaches on hemodynamics, combined with a shear stress exposure history model of platelets within a stenosed porcine bifurcation. Simulations used both single/multiphase blood models to determine which approach best predicts phenomena associated with atherosclerosis and atherothrombosis. A novel Lagrangian platelet tracking model was used to evaluate residence time and shear history of platelets indicating likely regions of thrombus formation. Results show a decrease in area of regions with pathologically low time-averaged WSS with the use of multiphase models, particularly in a stenotic bifurcation. Significant non-Newtonian effects were observed due to low-shear and varying hematocrit levels found on the outer walls of the bifurcation and distal to the stenosis. Platelet residence time increased 11% in the stenosed artery, with exposure times to low-shear sufficient for red blood cell aggregation (>1.5 s). increasing the risk of thrombosis. This shows stenotic artery hemodynamics are inherently non-Newtonian and multiphase, with variations in hematocrit (0.163-0.617) and elevated vorticity distal to stenosis (+15%) impairing the function of the endothelium via reduced time-averaged WSS regions, rheological properties and platelet activation/adhesion.

Biomechanics in thrombus formation from direct cellular simulations

Numerically reproducing the process of thrombus formation is highly desired for understanding its mechanism but still remains challenging due to the polydisperse feature of blood components and their multiple biochemical or biomechanical behaviors involved. We numerically implemented a simplified version of the process from the perspective of biomechanics, using a mesoscale particle-based method, smoothed dissipative particle dynamics-immersed boundary method. This version covers the adhesion and aggregation of platelets (PLTs), the deformation and aggregation of red blood cells (RBCs), and the interaction between PLTs and RBCs, as well as the blockage of microvessels. Four critical factors that can affect thrombus formation were investigated: the velocity of blood flow, the adhesive ability of PLTs, the interaction strength between PLTs and RBCs, and the deformability of RBCs. Increasing the velocity of blood flow was found to be the most effective way to reduce the microvessel blockage, and reducing the adhesive ability of PLTs is also a direct and efficient way. However, decreasing the interaction strength between PLTs and RBCs sometimes does not alleviate thrombus formation, and similarly, increasing the deformability of RBCs does not have a significant improvement for the severely blocked microvessel. These results imply that maintaining high-rate blood flow plays a crucial role in the prevention and treatment of thrombosis, which is even more effective than antiplatelet or anticoagulant drugs. The drugs or treatments concentrating on reducing the PLT-RBC interaction or softening the RBCs may not have a significant effect on the thrombosis.

Fracture mechanics analysis of fibrin fibers using mesoscale and continuum level methods

Computational models for simulating and predicting fibrin fiber fracture are important tools for studying bulk mechanical properties and mechanobiological response of fibrin networks in physiological conditions. In this work, we employed a new strategy to model the mechanical response of a single fibrin fiber using a collection of bundled protofibrils and modeled the time-dependent properties using discrete particle simulations. Using a systematic characterization of the parameters, this model can be used to mimic the elastic behavior of fibrin fibers accurately and also to simulate fibrin fiber fracture. In addition, a continuum model was modified and used to obtain the individual fibrin fiber fracture toughness properties. Using this model and the experimentally available fibrin mechanical properties, we predicted the range of fracture toughness (1 to k P a m ) values of a typical fibrin fiber of diameter 100 nm and its critical flaw size to rupture (~4 nm), both of which are not currently available in the literature. The models can be collectively used as a foundation for simulating the mechanical behavior of fibrin clots. Moreover, the tunable discrete mesoscopic model that was employed can be extended to simulate and estimate the mechanical properties of other biological or synthetic fibers.

Assessment of surface roughness and blood rheology on local coronary haemodynamics: a multi-scale computational fluid dynamics study

The surface roughness of the coronary artery is associated with the onset of atherosclerosis. The study applies, for the first time, the micro-scale variation of the artery surface to a 3D coronary model, investigating the impact on haemodynamic parameters which are indicators for atherosclerosis. The surface roughness of porcine coronary arteries have been detailed based on optical microscopy and implemented into a cylindrical section of coronary artery. Several approaches to rheology are compared to determine the benefits/limitations of both single and multiphase models for multi-scale geometry. Haemodynamic parameters averaged over the rough/smooth sections are similar; however, the rough surface experiences a much wider range, with maximum wall shear stress greater than 6 Pa compared to the approximately 3 Pa on the smooth segment. This suggests the smooth-walled assumption may neglect important near-wall haemodynamics. While rheological models lack sufficient definition to truly encompass the micro-scale effects occurring over the rough surface, single-phase models (Newtonian and non-Newtonian) provide numerically stable and comparable results to other coronary simulations. Multiphase models allow for phase interactions between plasma and red blood cells which is more suited to such multi-scale models. These models require additional physical laws to govern advection/aggregation of particulates in the near-wall region.

Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots was modeled by coupling atomistic simulation data and microscopic experimental data. We propose a new protofibril element composed of a nonlinear spring network, and constructed this based on molecular simulations and atomic force microscopy results to simulate the force extension behavior of fibrin fibers. This new network model also accounts for the complex interaction of protofibrils with one another, the effects of the presence of a solvent, Coulombic attraction, and other binding forces. The network model was formulated to simulate the force–extension mechanical behavior of single fibrin fibers from atomic force microscopy experiments, and shows good agreement. The validated fibrin fiber network model was then combined with a modified version of the Arruda–Boyce eight-chain model to estimate the force extension behavior of the fibrin clot at the continuum level, which shows very good correlation. The results show that our network model is able to predict the behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the break strain. We used the network model to explain why the mechanical response of fibrin clots and fibrin fibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.